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Select the correct answer. Ronald compared the rate at which water is used from two different water storage tanks by measuring the volume of the water remaining. The results are shown in the table. Time (hours) Tank 1 (gallons) Tank 2 (gallons) 0 300 300 1 240 260 2 192 220 3 153.6 180 4 122.88 140 Which statement best describes his results? A. The volume of tank 2 can be represented by an arithmetic sequence because the volumes in successive hours have a common difference. B. The volume of neither tank can be represented by an arithmetic sequence because the volumes in successive hours do not have a common ratio. C. The volume of both tanks can be represented by a geometric sequence because the volumes in successive hours have a common ratio. D. The volume of tank 1 can be represented by a geometric sequence because the volumes in successive hours have a common difference.

Respuesta :

Answer:

Step-by-step explanation:

C. The volume of both tanks can be represented by a geometric sequence because the volumes in successive hours have a common ratio.

reinhard10158

Answer:

A

Step-by-step explanation:

the tank 1 sequence is

300 240 192 153.6 122.88

to be a geometric sequence there must be a constant factor r that creates every term by multiplying r with the pervious term.

to go from 300 to 240 by multiplication, the factor r has to be 4/5 :

300 × 4/5 = 240

this has to be true for all the other terms too :

240 × 4/5 = 192 correct

192 × 4/5 = 153.6 correct

153.6 × 4/5 = 122.88 correct

so, this is indeed a geometric sequence with the common ratio r = 4/5.

the tank 2 sequence is

300 260 220 180 140

to be an arithmetic sequence there must be a constant difference between each pair of subsequent terms :

to go from 300 to 260 by addition/subtraction we need to subtract 40 (or add -40).

this has to be the case for all the other terms too :

260 - 40 = 220 correct

220 - 40 = 180 correct

180 - 40 = 140 correct

so, this is indeed an arithmetic sequence with the common difference of -40.

therefore,

A is correct.

B is incorrect also because it mixed up the conditions for geometric and arithmetic sequences.

C is incorrect

D is incorrect also because it mixed up the conditions for geometric and arithmetic sequences.

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